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How advanced mathematics and gaming theory can help you as a trader


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How advanced mathematics and gaming theory can help you as a trader

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  #101 (permalink)
 Fat Tails 
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Geomean View Post
I spent weeks studying Vince 8 years ago and setting up excell files of a 35+ year trading history to calculate optimum f on my personal trading history.

Well worth the effort, and it uncovered that my bet sizes were often way too big. It also reduced my overall market exposure, and confirmed a kind of anti-Martingale approach of the type Vince discusses in his "Leveraged Trading Space"

But even @ optimum f, I still didn't like the drawdowns, and the potential drawdowns, especially when trading in highly correlated assets in leveraged positions, although the run ups were exciting.

Then I found that adjusting optimum f for the biggest drawdown /size of loss I'm willing to suffer helped both my trading and my disposition.

Thus, I now use Optimum f % x total equity bet size/largest loss % =bet size/1% of equity. Such sizing also permitted more reliance on trading signals for exits rather than stops.

Then I increased the number of systems I traded and expanded the asset classes involved in an effort to reduce the overall correlation of the different bets in the portfolio.

Seems to work OK and add consistency, but there is more effort to time and monitor many more asset classes/positions, plus be worried about how everything seems to be correlated these days. A lot of work for a lone trader.

Indeed, a resource on correlation coefficients would be most helpful.

Geo

Thanks for this post!

Could you post one example which explains, how you have adapted Optimal F to comply with larger drawdowns?

For me the position sizing that results from Optimal F is still too aggressive, so if you discovered with Optimal F that your position sizing was too large, what leverage did you use before?

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  #102 (permalink)
 sharky 
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i have a roulette system that works if you have enough money and go to a table with no limits,its a red/black system,first you wait until 3 reds or black hit in a row,then you bet on the oppisite,if you win you take your money and wait for 3 of the same colors again and bet on the oppisite,if you lose you triple your money,so say you bet 20 bucks and lose then you bet 60 bucks,if you lose you bet 180 if you lose bet 540,on and on you get the pic,but you better have some cash and make sure your on a no limit table...sharky

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  #103 (permalink)
 sharky 
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was just thinking and no i havent tried but i wonder if that would work on trading if you have a loseing trade triple your money an the next entry?...sharky

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  #104 (permalink)
 worldwary 
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sharky View Post
was just thinking and no i havent tried but i wonder if that would work on trading if you have a loseing trade triple your money an the next entry?...sharky

It works until it doesn't, and then your account is blown.

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  #105 (permalink)
 Fat Tails 
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sharky View Post
i have a roulette system that works if you have enough money and go to a table with no limits,its a red/black system,first you wait until 3 reds or black hit in a row,then you bet on the oppisite,if you win you take your money and wait for 3 of the same colors again and bet on the oppisite,if you lose you triple your money,so say you bet 20 bucks and lose then you bet 60 bucks,if you lose you bet 180 if you lose bet 540,on and on you get the pic,but you better have some cash and make sure your on a no limit table...sharky

Sharky,

this does not work. You are a victim of the Gambler's Fallacy. There is no system in the world that will work with an even Roulette wheel. Only if you spot an uneven wheel, you may have an edge.

Tripling your money is a Martingaleapproach. This approach will typically get you many small wins and in the end a final large loss, which will exceed the aggregate wins.

You can look it up under

-> Gambler's Fallacy
-> Martingale

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  #106 (permalink)
 Fat Tails 
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sharky View Post
was just thinking and no i havent tried but i wonder if that would work on trading if you have a loseing trade triple your money an the next entry?...sharky

This would be progressive betting. If you increase your bet size after a losing trade, this is known as a Martingale strategy. It is one of the commonest mistakes of traders and known as averaging down.

Martingale approaches can work, if you have a trading approach, where the outcome of two consecutive trades are negatively correlated. However, it is not easy to show that this is the case.

When averaging down, you have a highly positive correlation of the trades. This can be understood, if you redefine the trades. This is what you would do

-> enter a position with contract size n
-> one the first position has lost a certain amount you add n contracts to your position

Now this is the same, as if

-> you had exited the first trade taking a loss
-> entering a new trade with contract size 2*n

If the old and the new trade are positively correlated, this is not a good decision. If there is a negative correlation, this strategy may give you an edge. However, this behavior is typically driven by loss aversion and not by correlation analysis and is known as one of the fastest roads to disaster.

Never average down any of your losses. Be a man and take the first loss.

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  #107 (permalink)
 PositiveDeviant 
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sharky View Post
i have a roulette system that works if you have enough money and go to a table with no limits,its a red/black system,first you wait until 3 reds or black hit in a row,then you bet on the oppisite,if you win you take your money and wait for 3 of the same colors again and bet on the oppisite,if you lose you triple your money,so say you bet 20 bucks and lose then you bet 60 bucks,if you lose you bet 180 if you lose bet 540,on and on you get the pic,but you better have some cash and make sure your on a no limit table...sharky

I used to do something similar, the odds of getting 4 red or black in a row are lower than a straight 3. I used to eyeball several tables at once waiting for them to come up.


Also, I found a site where you can calculate binomial probability distribution, as well as other types of cumulative probabilities - Statrek.com


Quoting 
What is a binomial distribution? A binomial distribution is a probability distribution. It refers to the probabilities associated with the number of successes in a binomial experiment.
For example, suppose we toss a coin three times and suppose we define Heads as a success. This binomial experiment has four possible outcomes: 0 Heads, 1 Head, 2 Heads, or 3 Heads. The probabilities associated with each possible outcome are an example of a binomial distribution.


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  #108 (permalink)
Nickemp
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Here is the problem with the roulette strategy. Even if there were such a thing as a casino that didn't limit bets you are effectively playing a game with a 47% chance of winning. That means you have a realistic probablilty of, at some stage, getting 16 losers in a row. See below for how much your last bet would be if you started with $20. Even if you could fund that bet your money would be better spent owning a casino rather than playing in one.

Your best bet is to never go to a casino. You would be better off buyng the occasional deep out of the money option like Nasim Taleb

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  #109 (permalink)
jlancaster
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When you go to a casino you have to go with a budget and you can't go over the budget. Its a weekend in Vegas kind of scenario. You go with $5k or $10k or whatever amount you're comfortable with that you can spend. If you can lose it without worrying too much you're fine. Just play and at the end of the weekend you either win or lose. If you do this many times over your lifetime, you're going to be in the negative.

The Law Of Large Numbers at work people.

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  #110 (permalink)
 Fat Tails 
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jlancaster View Post
When you go to a casino you have to go with a budget and you can't go over the budget. Its a weekend in Vegas kind of scenario. You go with $5k or $10k or whatever amount you're comfortable with that you can spend. If you can lose it without worrying too much you're fine. Just play and at the end of the weekend you either win or lose. If you do this many times over your lifetime, you're going to be in the negative.

The Law Of Large Numbers at work people.


Casino(1), Trading(2) or Opera(3): Entertainment will cost you some money.

Unless you are the House(1), have an edge that you exploit in a repetitive and boring manner(2), or you are one of the singers(3).


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  #111 (permalink)
 jungian 
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ENJOY!

Gambler's Ruin Java Applet

This applet simulates a gambler who repeatedly bets $10, until he either loses by going broke, or wins by doubling his initial fortune (Init).

The applet accepts the following keyboard inputs. (You may need to "click" on the applet first.)
  • Use the numbers '0' through '9' to set the animation speed level higher or lower.
  • Use 'r' to restart the simulation, or 'z' to zero the Win/Loss counts.
  • Use '>' and '<' to increase/decrease the win probability of each bet. (Possible values include 0.492929 [the probability of winning at craps] and 0.473684 [the probability of winning at roulette] plus various other values like 0.333333, 0.4, 0.45, 0.49, 0.495, 0.499, 0.4999, and 0.5.)
  • Use '+' and '-' to increase/decrease the initial fortune by $10 (and restart). Or, use 'T' or 'H' or 'G' or 'F' to set the initial fortune to $10 or $100 or $1000 or $5000, respectively.
  • Use 'A' to jump to $10 ahead of bankruptcy, or 'B' to jump to $10 behind victory.

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  #112 (permalink)
 PositiveDeviant 
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Geomean View Post
Indeed, a resource on correlation coefficients would be most helpful.

Geo

This might be what you're looking for; www.impactopia.com

You need to register for the side-by-side correlations and some other features, but it's free to do so.


Impactopia
We consider here about 4,500 US equities traded on the NYSE, AMEX, and Nasdaq markets. In order to compare the price fluctuations of those equities, we compute the correlations for all possible pairs, i.e. about 10 million pairs. The engine developed by Impactopia helps sorting out the millions of correlation coefficients. A user can query the database for calculating lists of top correlated pairs of stocks, lists of anticorrelated pairs, and lists of correlated stocks to any equity.


Here's another one - www.aistockcharts.com

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  #113 (permalink)
KonQuistador
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RM99 View Post
Okay, so I thought I'd contribute a little bit of wisdom or at least food for thought.

What would you say, if I told you that you can make money on a mutually exclusive, binomial event such as flipping a coin (50% probability)?

It blows most peoples minds when I tell them this. Here are the conditions......A) You must have control over the wager amount, B) You must have a significant starting capital (say 100x the initial wager amount) and C) You must adhere to a strict diet of progressive betting strategy.

Here's how it works: Progressive betting requires that it be truly mutually exclusive and also requires inherent "strings" be present over a given sample of n events.

Take for instance, our coin flip example. If you have a data sampling of say 10,000 flips. Over the course of that entire data set, you will experience both positive and negative strings. The distribution will follow an exponential decay (i.e. there will be a very small number of long strings and there will be a very large number of short strings.) A typical distribution for strings might look like this......10 strings 1, 9 strings 3, 8 strings 7, 7 strings 15, etc.

Ever wonder why typical profit analysis tools show strings? Here's how to make it work.

If the event is truly mutually exclusive and binomial, over large samplings, you'd expect the number of winning strings to be similar (negligibly identical) to losing strings.


So, you bet initally 10 units. If the outcome is a win, you take 50% of the profit and leave the other half out as an additional wager increase. If the next outcome is positive, you do the same, take 50% and leave the rest, again upping your wager. When you lose, you restart the wager sequence back to the original wager/lowest increment.

So over a string of 5 wins (10 unit start bet)....it would yield 65.9375 units of profit and the same losing string would yield a loss of 50 units.

The key to progressive betting is inherent strings. The system fails and you actually lose money if there are no strings and it's simply a binary oscillator (i.e. win, loss, win, loss, win, loss, etc).

This is exactly how successful blackjack betting strategies are employed.

The second part of this segment is second order effects and how even with a 50% probability and a "player" using progressive betting will still end up losing.

Maybe this those have some merit to a degree. I live about 30 min. from Oklahoma so this last weekend me and the wife decide to take a small drive over to Oklahoma to check out the Wyns Casino. I don't know how to play any cards game such as blackjack or texas hold em. Slot machines are a waste in my opinion so my game of choice was roulette. My game plan was to watch all the numbers that had come up recently so I wrote down the #'s that had come up more than once . Then what I did I wrote numbers that had not come up at all. Then Ipaired numbers together. All this while the wheel kept on spinning and new numbers would come up. When I had up to six pairs of numbers I was ready to begin. I placed my wagers up to 5 chips covering pairs of #s that had been hot and the ones that were cold. At first I won three wagers at once and was like this works but then a string of losses came up that almost took me out. Just when I was about to lose all my money I had strings of wins again that put me where I started. In a span of three hours I played with the same money I began while I saw people come and lose everything. My plan was simple but changing constantly oh and I had no alcohol in me either. At the end of the night I ended up flat...which is better than losing. So my probabilties on that night were at 50/50

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  #114 (permalink)
 Fat Tails 
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KonQuistador View Post
Maybe this those have some merit to a degree. I live about 30 min. from Oklahoma so this last weekend me and the wife decide to take a small drive over to Oklahoma to check out the Wyns Casino. I don't know how to play any cards game such as blackjack or texas hold em. Slot machines are a waste in my opinion so my game of choice was roulette. My game plan was to watch all the numbers that had come up recently so I wrote down the #'s that had come up more than once . Then what I did I wrote numbers that had not come up at all. Then Ipaired numbers together. All this while the wheel kept on spinning and new numbers would come up. When I had up to six pairs of numbers I was ready to begin. I placed my wagers up to 5 chips covering pairs of #s that had been hot and the ones that were cold. At first I won three wagers at once and was like this works but then a string of losses came up that almost took me out. Just when I was about to lose all my money I had strings of wins again that put me where I started. In a span of three hours I played with the same money I began while I saw people come and lose everything. My plan was simple but changing constantly oh and I had no alcohol in me either. At the end of the night I ended up flat...which is better than losing. So my probabilties on that night were at 50/50

If you play roulette, you have a negative expectancy. Your probabilities were less than 50/50. You simply did not play long enough to lose all your money.

In roulette there is no such thing as hot or cold numbers. Consecutive wheels runs are independent from each other, so the result of any run does not depend on the previous run.

Writing down numbers is a futile endeavor, as the outcome of the current run does not depend on previous runs. For further information check the "Gambler's Fallacy".

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  #115 (permalink)
KonQuistador
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Fat Tails View Post
If you play roulette, you have a negative expectancy. Your probabilities were less than 50/50. You simply did not play long enough to lose all your money.

In roulette there is no such thing as hot or cold numbers. Consecutive wheels runs are independent from each other, so the result of any run does not depend on the previous run.

Writing down numbers is a futile endeavor, as the outcome of the current run does not depend on previous runs. For further information check the "Gambler's Fallacy".

I don't know I played for about 3 hours straight with the same money. I have done this technique before in vegas and it worked for me their as well until I started drinking....lol. Im not saying that your going to beat the system but in my experience your odds at winning do get better.

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  #116 (permalink)
 Fat Tails 
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KonQuistador View Post
I don't know I played for about 3 hours straight with the same money. I have done this technique before in vegas and it worked for me their as well until I started drinking....lol. Im not saying that your going to beat the system but in my experience your odds at winning do get better.

Think about it again. Roulette is a sucker's game, because the only way to win is sheer luck.

Your "system" is funny, because it has no impact on the results.

It is like playing in a lottery. The odds are against you, but there will always be a winner.

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  #117 (permalink)
 whatnext 
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I've heard that Craps is the only percentage based casino game where you can alter the odds in your favor.

It stems from having physical control over the die while throwing them. Gamblers have practiced rolling with a specific number on each die facing upwards and another facing either right or left.

Casinos must be wise to the method if it has really worked well for some.

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  #118 (permalink)
KonQuistador
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Fat Tails View Post
Think about it again. Roulette is a sucker's game, because the only way to win is sheer luck.

Your "system" is funny, because it has no impact on the results.

It is like playing in a lottery. The odds are against you, but there will always be a winner.

Then im just a lucky man winning at a sucker's game... i like the sound of that.

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  #119 (permalink)
Geomean
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Fat Tails View Post
Thanks for this post!

Could you post one example which explains, how you have adapted Optimal F to comply with larger drawdowns?

For me the position sizing that results from Optimal F is still too aggressive, so if you discovered with Optimal F that your position sizing was too large, what leverage did you use before?

I pasted at the end of this post an Excel analysis of DAG data created based on real time publicly published signals and results from a popular candlestick trading system.

I've calculated the Optimum f bet size using that data.

Let's say one has 100K capital.

The DAG optimum f% under that system when buying is 22.92%, for a bet size of $22,920.

Historically, the largest buy loss is -9.4% and 9.4% of $22,920 optimum f bet size is $2,154, or 2.154% of the assumed 100K equity.

Adjusting the max optimum f% loss of 2.154%/$22,920 = 1%/x makes the bet size $10,640

A 9.4% loss on $10,640 is $1000.16, or 1% of the 100K equity

Note that the max 1% drawdown limitation cut the bet sizing by more than half for both the long and short side signals.

A max drawdown bet size limitation is a real benefit when trading multiple asset classes simultaneously.

Using this kind of limitation and adding systems and instruments can get one closer to what Vince describes in his recent Leveraged Trading Space.

Good luck!

DAG AGRICULTURE DOUBLE LONG ETN KELLY ANALYSISAGA is the 2X inverse but has no volume DYY is another double long commodities ETF

# Trades58#Wins#Losses# BUYS34# Buy Wins26#Buy Losses8Total Buy Gain437Av BUY Gain0.079629015Av BUY Loss-0.034470462Largest Buy Loss-9.400%Long BUY Winning Probability (W)0.764705882Long BUY Win/Loss Ratio ("R")2.310065194Long (BUY) Only Kelly %0.662849832Arithmetic Expected Return1.531226325Optimal f22.92%Opt f x Largest Loss as % of acct value-2%1% Portfolio Loss Opt f x Largest Loss Limit Bet Size10.64%Variance in Holding Period Returns0.008609919Standard Deviation Actual HPR's (no stop)0.092789648Multiplicative Growth Function (sq rt A2-S2)1.528412294TWR15324290.13# SELLS38# SELL WINS23# SELL LOSSES11AV SELL GAIN5.879%AV SELL LOSS-4.294%LARGEST SELL LOSS-15.080%Short (Sell) Winning Proability (W)0.605263158Short (Sell) Win/Loss Ratio ("R"1.369Short(Sell) Only Kelly %31.6955%Arithmetic Expected Return43.40%Optimal f15%Opt f x Maximum loss as % of acct value-2.32%1% Portfolio Loss Opt f x Largest Loss Limit Bet Size6.63%Variance in Holding Period Returns0.005242327Standard Deviation Actual HPR's (no stop)7%Multiplicative Growth Function (sq rt A2-S2)43%TWR6.81462E-13

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  #120 (permalink)
 Arpad 
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Fat Tails View Post
The Bet Size Modulator
The outcome of your bets are not influenced by or correlated to the bet size. If you have doubled your bet size this does not change the win rate of the following bet, so it just doubles your expectancy.

@Fat Tails,

This does not double your expectancy.

Expectancy =

(Average Profit * Probability of Winning) – (Average Loss * Probability of Losing)
–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––
Average Risk amount (or Average Loss)

So your expectancy in your example is always 0.2, regardless of bet size.
Expectancy is a measure of your trading system, it is based on Win Rate and Reward:Risk ratio, nothing else. It has nothing to do with bet size or position size percent.

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  #121 (permalink)
 Fat Tails 
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Arpad View Post
@Fat Tails,

This does not double your expectancy.

Expectancy =

(Average Profit * Probability of Winning) – (Average Loss * Probability of Losing)
–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––
Average Risk amount (or Average Loss)

So your expectancy in your example is always 0.2, regardless of bet size.
Expectancy is a measure of your trading system, it is based on Win Rate and Reward:Risk ratio, nothing else. It has nothing to do with bet size or position size percent.

Hi Arpad,

please look up the defintion of the expectancy (or mathematical expectation). You will find it in the trader's wiki here as well. It is not a ratio but an absolute value. The definition is

expectancy = winning probability * average winning trade - losing probability * average losing trade

This means that it is a $ amount. If you double your bet size this will neither change your winning nor your losing probability, but it will double the $ amount of your average winning trade and your average losing trade.

Doubling the bet size will therefore double your expectancy or mathematical expectation.

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  #122 (permalink)
 Arpad 
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You could look at expectancy as a measure of the average profit, as you say and as it is stated on the wiki of this website.
You could, if it makes sense. Probably it does.
However, another approach is at least as rational as the above:
the measure of your system, so what your systems money making capability is.

I came across the term expectancy while reading Van Tharp. He used the formula you have mentioned in the first edition of ‘Trade your way to financial freedom’, but he corrected it later.
So the formula cited by me in my previous post is from Van Tharp, after correction.

It makes more sense to me as a measure of ROI of your system.

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 Fat Tails 
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Arpad View Post
You could look at expectancy as a measure of the average profit, as you say and as it is stated on the wiki of this website.
You could, if it makes sense. Probably it does.
However, another approach is at least as rational as the above:
the measure of your system, so what your systems money making capability is.

I came across the term expectancy while reading Van Tharp. He used the formula you have mentioned in the first edition of ‘Trade your way to financial freedom’, but he corrected it later.
So the formula cited by me in my previous post is from Van Tharp, after correction.

It makes more sense to me as a measure of ROI of your system.

Hi Arpad,

thank you for your answer. As I have the 2nd edition of the book by van Tharp, I have checked his definitions for the expectancy. Indeed, he defines expectancy as the "mean R Multiple".

Mathematically, this is false. Mathematically the expectation is the arithmetic average of a random variable defined over a probability space. The expectation depends on two different factors

-> the winning probability
-> the size of the average winning trade versus the average losing trade

Now let us look at Van Tharp's definition. He divides the mathematical expectation by the factor, which is the amount risked, and declares that this is the expectancy. In doing so, he commits several errors:

(1) Let us look at his example with the marbles (pages 197 ff). He compares two cases with an "expectancy" of 0.2 R and 0.78 R. His results do not make sense, because he has selected R arbitrarily. In his first example all losing trades produce a loss of 1 R, in his second example the losers produce losses of 1, 2 and 3 R. This is totally inconsistent, as for the second case he should have used one of two possible approaches

(a) Define R as the maximum loss. In this case 3R becomes the real R and his "expectancy" should only be 0.26 R, and not 0.78 R

(b) Define R as the average loss (as you did in your definition). In this case 1.28 R becomes the real R and his "expectancy" should be 0.61 R

This was just to show that he does not properly use his own concept. Typically to evaluate any system you would rather use the maximum drawdown or loss within a given confidence limit rather than any average. So the second marble system may be still superior to the first, but Van Tharps results are false.

(2) If you look at a ratio - as van Tharp does - you introduce the concept of leverage. A reward-to-risk ratio assumes that a favorable ratio can be used to generate better returns than an approach with higher absolute returns, but a higher inherent risk. This is true if you use leverage. Once you decide to use leverage, the next question is how much leverage you use. The most common approach to this question is a fixed fractional position sizing, which is based on an optimal f, which in turn depends on the probability distribution.

Without going into further details, it can be shown that the performance of a system should be judged against the geometric mean of its returns. The geometric mean can be approximated by using the arithmetic mean and the standard deviation, which is a measure of dispersion. The concept of the R-Multiple does not correctly catch the dispersion of results, so basically the method can not produce any valid comparisons of two leveraged systems.

So at best Van Tharp introduces a set of simple ideas, such as the R-Multiple, which help beginning traders to overcome some of the psychological difficulties of trading, such as loss aversion. Loss aversion will let cut you profits short and let your losers run. Judging trades against R-Multiples is a highly effective medicine against loss aversion. The concepts presented by Van Tharp therefore have a high practical value as they address psychological difficulties faced by traders.

Mathematically his approach, the definitions and examples are mostly flawed.

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 Arpad 
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Hi Fat Tails,

Thanks for clarifying things.

In a later study Van Tharp introduced the System Quality Number:

SQN = (Expectancy / Standard Deviation of R) * square root of Number of Trades

You can choose a time period for the number of trades. It’s arbitrary.
It’s obvious if you have short time frame system it will look much better compared to a long time frame system. In one respect this is OK, because you want to know how much money can your system make in a given time period. On the other hand, you will not get a real measure of your system if you want to compare systems across categories, i.e. you want to compare a day trading system to a swing trading system.

However, I think you could omit the second part of the above equation, and use only SQN = (Expectancy / Standard Deviation of R).

But if you only observe one kind of systems (e.g. only swing trading systems based on daily close price, or only 5 min. day trading systems), you could use the complete formula:
· SQN = (Expectancy / Standard Deviation of R) * square root of Number of Trades
· or you could use the shortened formula SQN = (Expectancy / Standard Deviation of R) and Expectunity, which is Expectancy * Opportunity.
In fact these two are nearly the same.


What do you think?
What would be the best equation to measure a system?

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 Lornz 
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Arpad View Post

What do you think?
What would be the best equation to measure a system?

Trading account > Initial deposit = Profitable system

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 Fat Tails 
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Arpad View Post
Hi Fat Tails,

Thanks for clarifying things.

In a later study Van Tharp introduced the System Quality Number:

SQN = (Expectancy / Standard Deviation of R) * square root of Number of Trades

You can choose a time period for the number of trades. It’s arbitrary.
It’s obvious if you have short time frame system it will look much better compared to a long time frame system. In one respect this is OK, because you want to know how much money can your system make in a given time period. On the other hand, you will not get a real measure of your system if you want to compare systems across categories, i.e. you want to compare a day trading system to a swing trading system.

However, I think you could omit the second part of the above equation, and use only SQN = (Expectancy / Standard Deviation of R).

But if you only observe one kind of systems (e.g. only swing trading systems based on daily close price, or only 5 min. day trading systems), you could use the complete formula:
· SQN = (Expectancy / Standard Deviation of R) * square root of Number of Trades
· or you could use the shortened formula SQN = (Expectancy / Standard Deviation of R) and Expectunity, which is Expectancy * Opportunity.
In fact these two are nearly the same.


What do you think?
What would be the best equation to measure a system?

Van Tharp's definition of the System Quality Number uses his own definition of th expectancy, which is based on the R-multiples. As I have stated, I do not understand, what is R, it seems to be an arbitrary measure. So I am not familiar with his concept, and would first have to try to understand it.

If you look at any system - assuming that returns are reinvested and that position size is calculated on a fixed fractional basis - there are two parameters that should be used

(a) Return: geometrical mean of cumulated returns over the total holding period
(b) Risk: largest observed drawdown

The largest observed drawdown is not R, because it is the result of a string of (mostly) losing trades.

For the geometric mean I would use the following approximation: Geometric mean = SQRT (Arithmetic Mean x Arithmetic Mean - Variance). Divide this by the largest drawdown and you get a measure for the system quality. If you compare this to the formula of Van Tharp, it uses similar input variables!

SQN = E * SQRT(N) / (AL * SD)

RAGM = SQRT(E * E - SD * SD) / LDD

where

E = mathematical expectation
AL = average loss or R (as defined by Van Tharp)
SD = standard deviations of return
LDD = largest observed drawdown
N = number of trades

Criticism:

-> E/SD is not a good proxy for the geometric mean
-> AL is not a good proxy for the drawdown
-> SQRT(N) has been added to emphasize the sample size

The system quality number could be a rule of thumb method, rather than a method based on the risk adjusted geometric mean. But as I said before, I do not know how it was derived.

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 Silver Dragon 
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 sharky 
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well i think going to the casino is a waste of money unless your just going for pleasure,i spend my money at the movies or shopping so there really is no difference we are both doing something we enjoy,and @Fat Tails your a pretty smart guy...sharky

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dkrumholz
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I believe that you are 100% correct except for the fact that every table has a maximum bet, preventing an indefinite execution of the plan. The casino also has the right to refuse any bet.

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 gparkis 
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betting on binomial does work if:
1. your winns are greater then your losses.
2. you have a fixed number of trades a day.

The second part is the part most people can not deal with because they actual think they have some intelligent design that will beat world psychology.

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 Bermudan Option 
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I started out thinking Fat Tails was right and then I was thinking the rm99 was correct, and then I went back to Fat Tails at although I am only 3 1/2 pages in so far.

If a coin flips Heads 5x in a row, the chances of the next flip being Heads is 15% for example. However this percentage only applies to the string itself. At the end of the day, the chance of the next flip being Heads is still 50% because each flip is completed detached from the previous outcome.

At first glance, this realization appears to crap all over the idea of chart patterns but I believe that would be overstating the results because financial markets do not deal with inanimate objects like coins, but rather with entities that remember and consistently make the same errors (read: create bubbles). Chart patterns seem to represent a string of emotional reactions that are more likely to happen than a random occurrence. To what degree they predict, of course, is definitely up for interpretation.

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 monpere 
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Bermudan Option View Post
I started out thinking Fat Tails was right and then I was thinking the rm99 was correct, and then I went back to Fat Tails at although I am only 3 1/2 pages in so far.

If a coin flips Heads 5x in a row, the chances of the next flip being Heads is 15% for example. However this percentage only applies to the string itself. At the end of the day, the chance of the next flip being Heads is still 50% because each flip is completed detached from the previous outcome.

At first glance, this realization appears to crap all over the idea of chart patterns but I believe that would be overstating the results because financial markets do not deal with inanimate objects like coins, but rather with entities that remember and consistently make the same errors (read: create bubbles). Chart patterns seem to represent a string of emotional reactions that are more likely to happen than a random occurrence. To what degree they predict, of course, is definitely up for interpretation.

It's a nice theoretical discussion and all, but the only way you can compare trading the markets to a coin flip, is if you trade by closing your eyes, throwing a dart and see if it hits the 'buy' button or the 'sell' button.

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 HowardCohodas 
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monpere View Post
It's a nice theoretical discussion and all, but the only way you can compare trading the markets to a coin flip, is if you trade by closing your eyes, throwing a dart and see if it hits the 'buy' button or the 'sell' button.

Are any of you familiar with the random entry experiments that dealt exclusively with exit strategy?

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 Fat Tails 
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Are any of you familiar with the random entry experiments that dealt exclusively with exit strategy?

I remember several sources for test of a combination of random entries with a defined exit strategy.


(1) One of the first sources is the 1991 classic by Charles LeBeau / David Lucas: Technical Traders Guide to Computer Analysis of the Futures Markets (recommended read).

They present results for the following stop strategies:

5-day Parabolic
10-day Parabolic
3 day high-low
10-day high/low
RSI Trail
Key Reversal
Fixed Stop $ 500
Fixed Stop $ 1000
Volatility Stop (Chandelier)
Stochastic Cross
Profit Target $ 1000
Profit Target $ 2000

Do not expect too much, the topic is covered on a few pages. Also, I doubt that the results from 1990 can be applied to today's markets.


(2) A more detailed description can be found in Jeffrey Owen Katz / Donna L. McCormick: The Encyclopedia of Trading Strategies.

Part III of that book (about 70 pages) is dedicated to the study of exits.

The methodology they used was to test all entry strategies against a standard exit strategy which served as the benchmark exit. This standard exit used

- a money management stop (stop order)
- a profit target (limit order)
- a time-based exit (market order)

The standard exit was then tested against random entries. Afterwards they modified the standard exits and tested different exit strategies against random entries. The results were more or less deceiving.

I am not fond of testing exits without taking into account the entryies. Although I believe that exits are more important than entries, the appropriate exit strategy should take into account the chosen entry. A trendfollowing trade may work well in combination with a trailing stop, a short countertrade may require a fixed target.

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 cpi65 
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 Fat Tails 
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cpi65 View Post
A little knowledge is a dangerous thing.


Not as dangerous as no knowledge. And then it is not the question who has built the car, but who drives it.

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 HowardCohodas 
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I did some work on random entry many years back. IIRC, it showed that a good exit strategy alone was not satisfying because markets trend only about 20% of the time. (I read this somewhere, but can't remember the source.) I concluded that getting the entry right helped greatly and that getting it wrong was not overly harmful.

One of these days, I hope to resurrect that study and look at the current trading environment.

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 Big Mike 
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tradetree
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This is an interesting thread and I'm only half way through, but I had a question (I also see the thread hasn't had a post is some time so I hope it is not dead). There were posts that proposed that all trading systems, ie programmed rules that trade a market, will eventually fail. The implication, if I understood, was that you should not trade them. If this was the correct implication, then I would disagree for multiple reasons.

Lets say I have a daytrade system that is back-tested 2 years and walk-forward tested 1 year and has a positive expectancy of 1.5 in profit factor. Let's further assume that the net profit vs. drawdown is over a factor of 4, ie $16000 / $4000 = 4. In this case you have a clear indication of when the system is no longer working. If you perform a Monte Carlo simulation you will find a 96% chance that the system will never go above $10,000 in drawdown. Lets say you select $10,000 drawdown as the point that you dump the system. In the mean time, you trade the system and make $100,000 off of it. Then one day it hits the $10,000 drawdown and you are out. That still leaves you with $90,000 in net profit.

Now the upfront risk is very real, because clearly you could start trading the system and the day you start is the start of the $10,000 loss. So you have an up-front risk of loss. But the probability that you are going to hit the breaking point of the system when you randomly start using it is exceedingly low. Add to that a diversification strategy that uses multiple systems and you can reduce risk even more.

My point is that automatic back-tested trading systems can be very worthwhile. I was not sure if there was a criticism or dismissal of them in this thread? I also would love input on the idea of dumping the system if it hits the Monte Carlo 96% point?

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  #140 (permalink)
 nakachalet 
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Fat Tails View Post
If you have a binomial distribution, this indicates that the single events are stochastically independent, or otherwise put uncorrelated. In this case there is no progressive betting strategy, which will give you an edge.

Progressive betting strategies only make sense, if subsequent events are correlated. This is not the case with a coin flip. Your example is simply false. Sorry for my lack of diplomacy.

during 1980 when myself was still very young and magnanimous.... there were standing invitations from a few casinos in vegas.... at the roulette tables, practically every 3 hours or so, i would win 10 to 14 times in succession and during that same period of time, the house would also have a winning streak of 13-17 times in succession as well....

the strategy was to double up each subsequent losing bet....

the amount was staggering indeed, if you apply the math to it.... to the 14th losing bet....; starting with only 2 chips @ $25 per chip.... now, if you are other than dick and jane gamblers infrequently visiting the tables, the house would allow you to bet practically any which way that enthrill your senses....

the at the moment excitement would be enough to entice anyone to return to the table.... particularly coupling with all the freebies thrown in to the envy of all around.... yes, you are presented with everything a human would wish and dream about....

returning to this thread.... human feeble emotion and human inability to stay focus evenly from the first hour to the third hour.... would empty your six-figure acct; even if you have a superior betting strategy....: is my sad conclusion in its finality....

any one or any trader tries to claim or to propose or to postulate.... that gambling and trading are the same or even similar.... really is probably excel at neither....

trading and gambling are a world apart.... like water and oil.... (a one man experiences)

doubling, tripling, quading your longs or shorts as guru h loves to demonstrate in his $300 per month trading room.... could definitely be profitable.... as guru h has shown for several years. but he never advocates such technique to be used everyday. he reserves his extraordinary talent only for events such as of the last few weeks.... and when the voice from the pit was extraordinarily high and piercing to the ears....

yes, all is probable, possible and applicable.... but the question remains.... are we experienced enough to take advantage of all those extraordinary strategies at this moment in time in our trading arena.... and i have no doubt many of you among numerous of us.... are already reaping these benefits....

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 Fat Tails 
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returning to this thread.... human feeble emotion and human inability to stay focus evenly from the first hour to the third hour.... would empty your six-figure acct; even if you have a superior betting strategy....: is my sad conclusion in its finality....

This thread is about understanding that -as long as the wheel is even - there is no superior betting strategy for Roulette. The house will always win in the long run.

Roulette is a negative expectancy game. For this type of game there are two strategies that make sense.

(1) Do not bet. This is the best strategy.
(2) If you bet, bet only once. Your chance is still 47.4% to win.

Doubling up your bet sizes - a classical strategy known as Martingale - is one of the safest way to lose everything.

Emotions simply act as a catalyst. Emotions induce you to increase the size of your bets. This is what the house wants. The house will make an average return of 2.6 % on every bet. The higher the bets the more the house will win.

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 wldman 
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Do they have any wheels with just one green numba...a zero but no double zero? That is called French or European Roulette. Some "American" boards also have only one green. Then instead of 47.37% red or black and 5.26% green you'd have 48.65% chance red or black and 2.7% chance green. If you did a ratioed risk spread on red or black and green, even with two greens (pays 17:1) and bet all your money on a single spin I believe you have created the best possible scenerio. Is that incorrect? DB

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 Fat Tails 
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wldman View Post
Do they have any wheels with just one green numba...a zero but no double zero? That is called French or European Roulette. Some "American" boards also have only one green. Then instead of 47.37% red or black and 5.26% green you'd have 48.65% chance red or black and 2.7% chance green. If you did a ratioed risk spread on red or black and green, even with two greens (pays 17:1) and bet all your money on a single spin I believe you have created the best possible scenerio. Is that incorrect? DB

The mathematical expectancy for betting red, black or green is the same for a European bord. Betting $1 will yield

Red or Black : $ 1 * 18/37 - $ 1 * 19/37 = -1/37 = - 0.027 $
Green: $ 35 * 1/37 - $ 1 * 36/37 = -1/37 = - 0.027 $

Most other bets available on a roulette game have the same expectancy, although there a some bets that are even worse.

If I have to play, and I know that the expectancy is negative, my choice depends on the utility function. Best I do not play and just watch you playing. Every time I place a bet, this is mathematical nonsense, unless somebody else pays me for doing it or forces me to place a bet.

Under these circumstances, it is quite difficult to find a solution. Any solution adopted depends on the boundary conditions that somebody has imposed on me. If I am forced to play one time and bet everything at once, and if the total sum is an important part of my wealth, then I would try to go for a haircut. Easiest way to do so, would be to bet half on red and half on black. With a high probability, I will only lose 2.7% and keep the rest. In case that green comes up, I will take the profits, run away and never play Roulette again in my life.

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cedar
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Great thread. I read every page, excellent discussion of the mathematics of trading and gambling. I learned a lot.

Thank you all, especially to fat tails who patiently took the time to explain hard statistics.

Anyone wishing to further their study of the religion of statistics, I would highly recommend Jeff Ma's recent book 'The House Advantage'. Jeff was the original member of the MIT black jack team, both the book and the movie were based on him.

last year he gave an interesting talk, authors at google. If you like to look it up on youtube.

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 andy2001 
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If you want to have an edge betting on a 50 50 event such as a coin toss you will need to get odd of better than even money.

If you have odds of less than even money it will be a -ev bet. progrssive betting patterns will not change a -ev bet to a +ev bet it will just lead to lots of smaller wins followed by a bigger less freqent loss to offset it.

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 andy2001 
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As far roulette goes there is a way to get an edge playing roulette. You need a hidden computer which is used to track the ball. Normally relative to the zero a few times after is has been set in motion. This information can then be used to predict the area where the ball is more likely to fall.
If you do this in Nevada and get caught you will be breaking there anti device law and could go to jail. There was a group of players doing the in a UK casino a few years ago who were arrested but then released because they found not to have broken any UK law.

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  #147 (permalink)
 Fat Tails 
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andy2001 View Post
As far roulette goes there is a way to get an edge playing roulette. You need a hidden computer which is used to track the ball. Normally relative to the zero a few times after is has been set in motion. This information can then be used to predict the area where the ball is more likely to fall.
If you do this in Nevada and get caught you will be breaking there anti device law and could go to jail. There was a group of players doing the in a UK casino a few years ago who were arrested but then released because they found not to have broken any UK law.

Of course, if you measure speed and angular momentum of the ball after it has been released, then you may calculate an estimate of where it will stop. Not easy though, because you have to place your chips, after the ball has been released.

Typically this type of information is disseminated by sellers of so-called roulette computers. As there is no system conceivable to beat the house, the greed of the gamblers can only be exploited by selling them cheating devices.

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  #148 (permalink)
 nakachalet 
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Fat Tails View Post
Of course, if you measure speed and angular momentum of the ball after it has been released, then you may calculate an estimate of where it will stop. Not easy though, because you have to place your chips, after the ball has been released.

Typically this type of information is disseminated by sellers of so-called roulette computers. As there is no system conceivable to beat the house, the greed of the gamblers can only be exploited by selling them cheating devices.

excuse me, fat tails,

your bets have to be in place BEFORE the ball is being rolled, snapped or shot out....

otherwise, your bets would be kindly and courteously and politely removed with an invitation to place your bets in the next round....

let's go and break their banks sometimes alright, fat tails. thx for all your previous assistance, much appreciated.

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  #149 (permalink)
 Fat Tails 
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nakachalet View Post
excuse me, fat tails,

your bets have to be in place BEFORE the ball is being rolled, snapped or shot out....

This depends on the rules of the casino. You may not place any bet after the "rien ne va plus", and this may be well after the ball has started to roll. Otherwise there would be no reason for using any cheating devices.

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 andy2001 
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nakachalet View Post
excuse me, fat tails,

your bets have to be in place BEFORE the ball is being rolled, snapped or shot out....

otherwise, your bets would be kindly and courteously and politely removed with an invitation to place your bets in the next round....

let's go and break their banks sometimes alright, fat tails. thx for all your previous assistance, much appreciated.


This is not correct. Most casinos allow bets to be made for some time after the ball is in motion.

I think my initial statement on how this is done is slightly inaccurate as the ball and the wheel need to be cloaked separately.

Below are some links about the gang that won about £1.3 million in 2 days in London. They got arrested but where found to have done nothing illegal so ended up keeping the money.

BBC NEWS | UK | England | London | Arrests follow £1m roulette win
The sting: did gang really use a laser, phone and a computer to take the Ritz for £1.3m? | UK news | The Guardian
BBC NEWS | UK | 'Laser scam' gamblers to keep £1m

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 nakachalet 
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andy2001 View Post
This is not correct. Most casinos allow bets to be made for some time after the ball is in motion.

I think my initial statement on how this is done is slightly inaccurate as the ball and the wheel need to be cloaked separately.

Below are some links about the gang that won about £1.3 million in 2 days in London. They got arrested but where found to have done nothing illegal so ended up keeping the money.

BBC NEWS | UK | England | London | Arrests follow £1m roulette win
The sting: did gang really use a laser, phone and a computer to take the Ritz for £1.3m? | UK news | The Guardian
BBC NEWS | UK | 'Laser scam' gamblers to keep £1m

just what do you mean 'most casinos'?

casinos by your neighborhood? run by entities perhaps unlicensed by the gaming commissions?

just try to place a bet after the ball is snapped, in atlantic city, reno, las vegas or the likes....

perhaps, i ought to be more tolerant, realizing that there are individuals who are frequent guests who are allowed to place their bets unconventionally.... and who are also allowed to just sign on the 'markers' without having to show any cash, to bet on anything and everything.... to their hearts' contents....

furthermore, if you were one of those, you could also eat what you like and when you like without anyone asking you or bothering you....

sound good? your companion also is afforded with the same courtesy with free show and what not....

before i forget, cause i've not done it for a long while now, you would also be able to fly first class, airline of your own choosing, at the casinos' expense....

i could almost guarantee that you would have a good time, a great time, or even the best time of your life.... if you like partying and that sort of life style....

interested....?

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 andy2001 
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nakachalet View Post
just what do you mean 'most casinos'?

casinos by your neighborhood? run by entities perhaps unlicensed by the gaming commissions?

just try to place a bet after the ball is snapped, in atlantic city, reno, las vegas or the likes....

perhaps, i ought to be more tolerant, realizing that there are individuals who are frequent guests who are allowed to place their bets unconventionally.... and who are also allowed to just sign on the 'markers' without having to show any cash, to bet on anything and everything.... to their hearts' contents....

furthermore, if you were one of those, you could also eat what you like and when you like without anyone asking you or bothering you....

sound good? your companion also is afforded with the same courtesy with free show and what not....

before i forget, cause i've not done it for a long while now, you would also be able to fly first class, airline of your own choosing, at the casinos' expense....

i could almost guarantee that you would have a good time, a great time, or even the best time of your life.... if you like partying and that sort of life style....

interested....?









As far I know there are no unlicensed casinos in the UK where I live. I went to two casinos in London last year and the end of 2009 to play poker. The Empire casino which is the largest in the UK gave me 2 or 3 coupons which could not be used at the poker table so I used them to bet black or red on roulette with a large edge over the casino as they were paying for half the bets.
As far as I remember bets where allowed after the ball was in motion.

As far as U.S casinos I have not been in them since my card counting days about 14 years ago. All the U.S casinos I went to where in Las Vegas, Laughlin, Reno or Stateline Nevada. As far as I remember bets after the ball is in motion you were allowed but I was not paying much attention to the roulette table, as I was there to play blackjack. I did get 2 room comps and lots of food comps and backed off from about 18 Nevada casinos while doing so. Along with already having been banned from a bunch of UK Casinos.

For more recent info on if bets are allowed after the ball is in motion in U.S casinos maybe try this link. It seems one person agrees with you on the Atlantic City casinos, but the consensus is you can bet after the ball is in motion.


http://wizardofvegas.com/forum/gambling/tables/2825-the-truth-in-a-way-the-past-numbers-to-have-hit-do-matter/6/

The reason most casinos will let you be after the ball is in motion is because they would lose far more money in bets not made from squares than they will save from the the very few players that may have working computers.

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  #153 (permalink)
traitor786
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RM99 View Post
Okay, so I thought I'd contribute a little bit of wisdom or at least food for thought.

What would you say, if I told you that you can make money on a mutually exclusive, binomial event such as flipping a coin (50% probability)?
.

intresting, I did this once with a deck of cards looking at red and black minus the jokers. Essentially a coin toss that quickly averages out to a 50-50.



every time a red card popped out i calculated minus 1 and every time a black card popped up I added 1. Intrestingly the max integer was -8/+8 meaning wagering when there were 8 more blacks that popped out then reds yielded the highest probability win

At the casino i simplified it as it was more of an enjoyment thing. I played black jack. with out really trying to read the table i played the same way a dealer would play giving me about 50-50% odds minus the initial payment i would put down to play. I would bet the minimum until the dealer lost twice in a row and then bet heavy ( to make negligible the initial payments to play and any other advantage the casino may have.

Not much of a gambler so only tried it twice both of which were profitable. Though i believe there was some luck involved as i dont really believe that a 2 streak lose justified a win and also there was no accounting for winning or loosing streaks like there was in the flipping cards. Needless to say i raised alot of eyebrows with the other players betting minimum and then out of no where raising to the max. the staff was on my case and they ended up closing the table lol.

Like my trading I simplified my strategy and estimated money management

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  #154 (permalink)
 nakachalet 
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traitor786 View Post
intresting, I did this once with a deck of cards looking at red and black minus the jokers. Essentially a coin toss that quickly averages out to a 50-50.



every time a red card popped out i calculated minus 1 and every time a black card popped up I added 1. Intrestingly the max integer was -8/+8 meaning wagering when there were 8 more blacks that popped out then reds yielded the highest probability win

At the casino i simplified it as it was more of an enjoyment thing. I played black jack. with out really trying to read the table i played the same way a dealer would play giving me about 50-50% odds minus the initial payment i would put down to play. I would bet the minimum until the dealer lost twice in a row and then bet heavy ( to make negligible the initial payments to play and any other advantage the casino may have.

Not much of a gambler so only tried it twice both of which were profitable. Though i believe there was some luck involved as i dont really believe that a 2 streak lose justified a win and also there was no accounting for winning or loosing streaks like there was in the flipping cards. Needless to say i raised alot of eyebrows with the other players betting minimum and then out of no where raising to the max. the staff was on my case and they ended up closing the table lol.

Like my trading I simplified my strategy and estimated money management

just curious, what kinds of setup do you use for your trading then? thx

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 Loren 
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Interesting discussion. One huge advantage the casino enjoys is the maximum bet limit they place on most games. This limit will ultimately be reached if you are increasing your bet to recoup prior losses on previous wagers. This limit is the ultimate casino edge.

There is no such edge in trading futures. The amount you wager is up to you limited only by your account size.

Other factors of course enter into this. If you suffer a string of losses whic will require you to trade more and more contracts to recoup your losses the liquidity of the contract being traded must be considered.

There are ways to mitigate even this if you trade index futures by being willing to trade multiple markets if the number of contracts necessary to recoup becomes an issue with liquidity.

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 Fat Tails 
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I have recently bought this book and it looks quite interesting.

Richard A. Epstein: The Theory of Gambling and Statistical Logic, Second Edition

"A background in upper-level undergraduate mathematics is helpful for understanding this work."







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traitor786
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Fat Tails View Post
If you play roulette, you have a negative expectancy. Your probabilities were less than 50/50. You simply did not play long enough to lose all your money.

In roulette there is no such thing as hot or cold numbers. Consecutive wheels runs are independent from each other, so the result of any run does not depend on the previous run.

Writing down numbers is a futile endeavor, as the outcome of the current run does not depend on previous runs. For further information check the "Gambler's Fallacy".

funny you mention this. i had a similar conversation with some one. I believe it is some what similar and if so then it questions your "Gamblers fallacy"

The idea was that the odds of a coin toss are 50-50 but the odds of getting 3 heads off the bat are smaller then 50-50. they are actually .5 x .5 x .5 = 0.215 this would mean that they are not independent from one another and they accumulate value.

Its arguable but the nail in the coffin is the Quebec lotto 6/49. Here you choose 6 numbers 1 to 49

so for example your 6 numbers could be 2, 40,20,33,39, 8

Odds of picking the correct number is 1/49 for the first one. 1/49 for the second and so forth. so it would be 1/49 to the power of 6 i believe.

If the numbers stand alone, the odds of winning the millions would be 1/49 ?

i agree that the odds of your second number being a 40 is 1/49 and the odds of the third being 20 is 1/49 ect. but the odds of all the numbers coming up we need to multiply

now lets say we have a grid of 9 surprise boxes. 3x3

there is a surprise in 3 of the boxes (one in each column) and there is also snake in one of the boxes.

the odds of hitting the snake are 1/9

the odds of getting all 3 surprises is about 3 times harder.

My example may not relate well or there may be something im not looking at here ?

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 Fat Tails 
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traitor786 View Post
funny you mention this. i had a similar conversation with some one. I believe it is some what similar and if so then it questions your "Gamblers fallacy"

The idea was that the odds of a coin toss are 50-50 but the odds of getting 3 heads off the bat are smaller then 50-50. they are actually .5 x .5 x .5 = 0.215 this would mean that they are not independent from one another and they accumulate value.

Its arguable but the nail in the coffin is the Quebec lotto 6/49. Here you choose 6 numbers 1 to 49

so for example your 6 numbers could be 2, 40,20,33,39, 8

Odds of picking the correct number is 1/49 for the first one. 1/49 for the second and so forth. so it would be 1/49 to the power of 6 i believe.

If the numbers stand alone, the odds of winning the millions would be 1/49 ?

i agree that the odds of your second number being a 40 is 1/49 and the odds of the third being 20 is 1/49 ect. but the odds of all the numbers coming up we need to multiply

now lets say we have a grid of 9 surprise boxes. 3x3

there is a surprise in 3 of the boxes (one in each column) and there is also snake in one of the boxes.

the odds of hitting the snake are 1/9

the odds of getting all 3 surprises is about 3 times harder.

My example may not relate well or there may be something im not looking at here ?

If you have a regular coin and throw it 3 times, each toss is independent from the prior toss - the coin does not have a memory - and the probabability of getting 3 heads in a row is

0.5 x 0.5 x 0.5 = 0.125

Nothing really difficult to understand.

The fallacy is to assume that if you had 10 heads in a row this will increase the odds to get tails in the 11th toss. This is not the case.

Many progressive betting systems are based on the gambler's fallacy. The grandfather of progressive betting was Jean-Baptiste le Rond d'Alembert (1717 - 1783) . A renowned physician and philosopher, he also had a keen interest in gambling and suggested a number of progressive betting systems that did not work.

The key to understanding progressive betting is that it will only work, if the probability of consecutive events depends on prior events, which means that they are stochastically dependent on each other.

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 Lornz 
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Fat Tails View Post
If you have a regular coin and throw it 3 times, each toss is independent from the prior toss - the coin does not have a memory - and the probabability of getting 3 heads in a row is

0.5 x 0.5 * 0.5 = 0.125

Nothing really difficult to understand.

The fallacy is to assume that if you had 10 heads in a row this will increase the odds to get tails in the 11th toss. This is not the case.

Many progressive betting systems are based on the gambler's fallacy. The grandfather of progressive betting was Jean-Baptiste le Rond d'Alembert (1717 - 1783) . A renowned physician and philosopher, he also had a keen interest in gambling and suggested a number of progressive betting systems that did not work.

The key to understanding progressive betting is that it will only work, if the probability of consecutive events depends on prior events, which means that they are stochastically dependent on each other.

Well, one only needs to double every bet until one gets it right, and then one will end up with one more unit than the original bet. This works as long as there's no limit on betting, and one has more money than God!

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  #160 (permalink)
 Lampert 
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I liked reading this thread, especially @Fat Tails rock-solid explanations about the gambler's fallacy. The summary in post #2 is also helpful.

If some still believe that strings of outcomes and progressive betting are beneficial for independent events, perhaps the following charts can help. I expanded on the spreadsheet provided by @worldwary in post #47.

This first chart shows 10 trials with a constant betting strategy (coin flips with 50/50 W/L). The initial capital is $100 and every bet is $10.




This second chart shows 10 trials with the same scenario, except that bets are increased by 50% after each win - ie. bets are increased during strings of wins. After each loss, the bet is returned to $10. The average bet is $13.34. This is the anti-martingale system or the "progressive string strategy" as described by the OP.




Just for interest, this chart shows one of the trials with three strings of 10 wins.




This last chart shows the distributions of final capital from 500 trials of each of the two betting strategies. Results from the progressive betting strategy have been normalized to match the bets used in the constant betting strategy (each final capital x 10.00 / 13.34). The binomial distributions are quite similar and their averages are close to the initial capital of $100. In other words, there is no benefit from the progressive betting strategy.




On the positive side, these charts show that one should be able to play a 50/50 game for a long time given a reasonable initial capital.

The spreadsheet is attached if anyone is interested.


Len

Attached Files
Register to download File Type: rar String Bet Experiment.rar (11.58 MB, 14 views)
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 Big Mike 
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Lampert View Post
The spreadsheet is too large to post (16 MB) but I can send if you PM me.


Len

Just zip it then attach it.

Mike

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  #162 (permalink)
traitor786
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nakachalet View Post
just curious, what kinds of setup do you use for your trading then? thx

I use Andrews pitchfork. Many dont like this kind of stuff but as it is all i have really learnt I love it, Its funny how when ever i see a chart some one posts price seems to just fly all over the indicator but with forks everything looks like its bouncing in the right place.

When I was trading in an office I remember listening to the squack. Here you can hear when Goldman Sachs makes a move. Many times I notice that they buy and sell at key points that i also use just they do so more selectively.

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  #163 (permalink)
traitor786
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Lampert View Post
I liked reading this thread, especially @Fat Tails rock-solid explanations about the gambler's fallacy. The summary in post #2 is also helpful.

If some still believe that strings of outcomes and progressive betting are beneficial for independent events, perhaps the following charts can help. I expanded on the spreadsheet provided by @worldwary in post #47.

This first chart shows 10 trials with a constant betting strategy (coin flips with 50/50 W/L). The initial capital is $100 and every bet is $10.




This second chart shows 10 trials with the same scenario, except that bets are increased by 50% after each win - ie. bets are increased during strings of wins. After each loss, the bet is returned to $10. The average bet is $13.34. This is the anti-martingale system or the "progressive string strategy" as described by the OP.




Just for interest, this chart shows one of the trials with three strings of 10 wins.




This last chart shows the distributions of final capital from 500 trials of each of the two betting strategies. Results from the progressive betting strategy have been normalized to match the bets used in the constant betting strategy (each final capital x 10.00 / 13.34). The binomial distributions are quite similar and their averages are close to the initial capital of $100. In other words, there is no benefit from the progressive betting strategy.




On the positive side, these charts show that one should be able to play a 50/50 game for a long time given a reasonable initial capital.

The spreadsheet is attached if anyone is interested.


Len



Your charts seem to disprove what i think fat tails is saying.

From my understanding Fat tails suggests that every toss is independent of the previous one. Yet he says that the odds of having 3 tails in a row is .5 x.5x.5

Maybe i havent thought about enough but it seems that as the string gets longer the "chances of having another head after a streak of heads is getting slimmer.

the chart where there is an increased bet placed after a string shows that it favours profit. from what i remember the negative was 2000 but the max positive was 3000, this could be luck but who knows. Even that one line that goes to the 3000 dollar line can be some thing that can be played. If you were to bet a chart like that over and over and favoured the buy side you'd end up really happy i think. In esence its a the "slight edge" we may all look for in trading. But yes it could be a big anomaly but in general there anomalies are wiped out over many runs.


also the other (i think last chart) shows something similar to my previous mentioned card flipping idea. and that is that there is a maximum to how big a string can get. which means that there is some form of "memory" as you call it.


Seems to me, some one who sah not really looked as deeply in to this as yourselves that you are backing up 2 opposing theories.

1. the odds decrease as strings go on (seen mathamatically) .5 x .5 x .5 = less then .5
2. solid objects dont have memory ?

and the second theory is where your logic seems to come from. There is no math or science there, the word memory was just used for lack of a better word and this makes it even more believable as only living things can have memory.

If things are not dependant on previous flips there would be no reason to revert back to the 50 50. if we do revert back to the 50 50 over many tries this indicates that previous flips must be accounted for in order to get back to the 50 50. That is to say the coin must keep a memory in order to revert to a certain percentage.

now again, i haven't really learnt all about this stuff, this is just my opinion which is usually wrong and not from any research. I'm sure some math genius has figured this all out. but untill i read it (when i have time as im very focused on trading right now) and i truely understand it then and find that the words used in the conclusion match the math ( this is usually where there is an issue in science) then Ill be happy to be better informed

randomness (50-50) can be charted and the randomness disapears as seen on your charts. step back they all look very symetrical (except the one where bet was increased).

I'll probably change my position on this as the convo goes on or i read past posts/links im sure

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  #164 (permalink)
 vvhg 
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The answer is already in your post:


traitor786 View Post
1. the odds decrease as strings go on (seen mathamatically) .5 x .5 x .5 = less then .5

To arrive at the chance of three heads in a row you multiply .5 three times. If you now want to calculate the chance of 4 heads in a row you just extend the string by *.5. this proves that the single event has got a .5 chance in order to give the 4 heads in a row event the chance of .5*.5*.5*.5


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  #165 (permalink)
traitor786
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vvhg View Post
The answer is already in your post:



To arrive at the chance of three heads in a row you multiply .5 three times. If you now want to calculate the chance of 4 heads in a row you just extend the string by *.5. this proves that the single event has got a .5 chance in order to give the 4 heads in a row event the chance of .5*.5*.5*.5


vvhg

yes but the last flip is a single event. even though it is part of the string. I imagine that the falasy would say state that the last flip has in a string has a 50 50 chance. the fact that the we mutiply the odds togeteher to get a smaller the 50 50 i would imagine is common sence?

I cant even tell what side your on.

the question should be.

if a coin is fliped 3 times , and 2 heads show up, what are the chances that the next flip comes a head also.

since the last flip has not been made, do we just assume it is an individual flip at 50 50 or do we look at the previous flips and say that it is .5 to the power of 3 ?

In order for it to be a falasy it should go against common sence to some respect and common sence would state that the last flip is not a 50 50.\

if you believe the last flip is a 50 5o, then all flips are 50 50.

if that the case then why do we even quote the formulae .5x..5 x .5 ?

maybe im just unclear on what side you are on or maybe im not understanding something here

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  #166 (permalink)
 vvhg 
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traitor786 View Post
yes but the last flip is a single event. even though it is part of the string. I imagine that the falasy would say state that the last flip has in a string has a 50 50 chance. the fact that the we mutiply the odds togeteher to get a smaller the 50 50 i would imagine is common sence?

I cant even tell what side your on.

the question should be.

if a coin is fliped 3 times , and 2 heads show up, what are the chances that the next flip comes a head also.

since the last flip has not been made, do we just assume it is an individual flip at 50 50 or do we look at the previous flips and say that it is .5 to the power of 3 ?

In order for it to be a falasy it should go against common sence to some respect and common sence would state that the last flip is not a 50 50.\

if you believe the last flip is a 50 5o, then all flips are 50 50.

if that the case then why do we even quote the formulae .5x..5 x .5 ?

maybe im just unclear on what side you are on or maybe im not understanding something here

All tosses are .5, and that is not my belief, it is the very definition of a fair coin toss.
If the last toss was not .5 how could we then calculate the exact probability of the string by .5^n?
Doesn't this clearly prove that each individual coin toss is .5? Otherwise the calculation wouldn't work.

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 Fat Tails 
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traitor786 View Post
Your charts seem to disprove what i think fat tails is saying.

From my understanding Fat tails suggests that every toss is independent of the previous one. Yet he says that the odds of having 3 tails in a row is .5 x.5x.5

The charts do not disprove independency. The odds for having 3 tails in a row are .5 x .5 x .5 = .125, because the tosses are independent.


traitor786 View Post
also the other (i think last chart) shows something similar to my previous mentioned card flipping idea. and that is that there is a maximum to how big a string can get. which means that there is some form of "memory" as you call it.

This is a fallacy. There is no maximum. However, the probability for a long string is inferior than the probability for a short string. If you want to get 10 tails in a row, the probability calculates as 1/1024. This means that statistically you need to run 1024 experiments of tossing a coin 10 times to observe the event "10 tails in a row" once. Even with 1024 experiments, it is not sure that you will observe the event, as there are random elements that contribute to the outcome.


traitor786 View Post
1. the odds decrease as strings go on (seen mathamatically) .5 x .5 x .5 = less then .5
2. solid objects dont have memory ?

The odds do not decrease, the odds for a single toss remain at 0.5. The calculated probability for three tosses in a row is larger than the calculated probabilibty for 4 tosses. This means that the probability depends on the number of consecutive tosses, but it does not decrease.

Objects do not have a memory,. If you have somebody who cheats when throwing the coin - consider that guy has a memory how he manipulated the previous toss - then there may well be a dependency between 2 consecutive events.

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 Lornz 
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All this discussion about coin flips reminded me of this:

https://www.espenhaug.com/ScientificCoinFlipExperiment.pdf

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 Fat Tails 
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Lornz View Post
All this discussion about coin flips reminded me of this:

https://www.espenhaug.com/ScientificCoinFlipExperiment.pdf



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 vvhg 
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 kronie 
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I thought this thread was about the complex relationship of mathematics to technical analysis (which is simply applied math customized towards trading)

instead, this thread is about the Random Walk Theory, and other related concepts the Vegas Odds Betters use to underlie their theories of placing bets and expected / anticipated odds outcomes.

Its amazing how many professional gamblers are also stock / bond / currency traders.

I guess Risk loves Risk and a "Fisherman always sees another Fisherman from afar" (who said that quote?)

Hint: Gordon Geckko ("Wall Street, Money Never Sleeps")

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 devdas 
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When One consider "String", it should be clear what is the Collection Size.
Problems with strings are , their collection is of virtually infinite size and there is no end, and any probabilities measure relying on assumption of finite collection size will not be correct.
Say with strings..in continuous tosses,

......H H H T T H H H H H T H T H H T T T H H H .......

1) I saw the Strings in Red color and yea, they are with Teal color also.

2) Opps, i saw two Black H before 3 Red H...yea its another H H H H H string
3 Teal H have 3 Black T prior to that....its another string....

there would be no end, and new strings can be obvious by unlimited combination. Why limit , to think 10 winning bets continuous is a string , before that 2 loosing bet might also make combination of 12 bet string....

Now saying probability of getting 3 H or 4 H...one is confining the collection size to limited numbers and that make sense to probabilities in that finite collection.

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 Fat Tails 
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vvhg View Post
But if you find the box, don't open it! You might half kill the cat...


vvhg

If I look at your avatar, I understand why you don't want to open the box.

Half-cats that have been sitting in a box for a while tend to be hungry.

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 Fat Tails 
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devdas View Post
When One consider "String", it should be clear what is the Collection Size.
Problems with strings are , their collection is of virtually infinite size and there is no end, and any probabilities measure relying on assumption of finite collection size will not be correct.
Say with strings..in continuous tosses,

......H H H T T H H H H H T H T H H T T T H H H .......

1) I saw the Strings in Red color and yea, they are with Teal color also.

2) Opps, i saw two Black H before 3 Red H...yea its another H H H H H string
3 Teal H have 3 Black T prior to that....its another string....

there would be no end, and new strings can be obvious by unlimited combination. Why limit , to think 10 winning bets continuous is a string , before that 2 loosing bet might also make combination of 12 bet string....

Now saying probability of getting 3 H or 4 H...one is confining the collection size to limited numbers and that make sense to probabilities in that finite collection.

Thanks for pointing this out. Of course, if you talk about a probability, you first need to specify the design of the experiment - or the rules of the game that you want to play.

With the toin cosses I assumed that you play one game as long as there is no heads. With this defintion every becomes a series of N tosses of tails and 1 heads, where the heads finishes the game.
Potential outcomes with a regular coin are

- H (no tail) -> probability 50%
- TH (one tail) -> probability 25%
- TTH (two tails) -> probability 12.5%

This definition of the game does not require a finite collection.

If you play a continuous tossing game and you look at the probability that the series of the last N tosses all resulted in tails X X X X X T T T , where X means anything (could be either T or H), then the probabilities of two consecutive events are dependent.

If you had a string of 3 Tails on event no. 1235, this conditions event no. 1236, as the chances to get another 3 tails in a row are now enhanced, if you know that the preceding 2 tosses resulted in tails. This is a conditional probability, and can be calculated by using the formula of Bayes.

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 devdas 
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Fat Tails View Post
..... play one game as long as there is no heads. With this defintion every becomes a series of N tosses of tails and 1 heads, where the heads finishes the game.
Potential outcomes with a regular coin are

- H (no tail) -> probability 50%
- TH (one tail) -> probability 25%
- TTH (two tails) -> probability 12.5%
...................................................
....................................................
.....................................................
........infinite strings decreasing with probabilities.


This definition of the game does not require a finite collection.

...... Beyes.

Thanx for example, i had enjoyed these in my schooling.
When we set rule "as long as"...it make collection itself infinite.
We can get each new string with decreasing probabilities as pointed out by 3 first strings.

If i remember correctly Beyes Theorem is also on Finite Collection size...

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Fat Tails View Post
Thanks for pointing this out. Of course, if you talk about a probability, you first need to specify the design of the experiment - or the rules of the game that you want to play.

With the toin cosses I assumed that you play one game as long as there is no heads. With this defintion every becomes a series of N tosses of tails and 1 heads, where the heads finishes the game.
Potential outcomes with a regular coin are

- H (no tail) -> probability 50%
- TH (one tail) -> probability 25%
- TTH (two tails) -> probability 12.5%

This definition of the game does not require a finite collection.

If you play a continuous tossing game and you look at the probability that the series of the last N tosses all resulted in tails X X X X X T T T , where X means anything (could be either T or H), then the probabilities of two consecutive events are dependent.

If you had a string of 3 Tails on event no. 1235, this conditions event no. 1236, as the chances to get another 3 tails in a row are now enhanced, if you know that the preceding 2 tosses resulted in tails. This is a conditional probability, and can be calculated by using the formula of Beyes.

Now you confused them completely.... Wait and see...

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 devdas 
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vvhg View Post
Now you confused them completely.... Wait and see...

vvhg


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  #178 (permalink)
 devdas 
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See, this is how, your game will compares with Infinite Cells of resistances...removing any number of cells doesn't changes the net resistance between points A and B.
What it simulates in given toss example....if one remove diagonally Ts...it will still have "Fresh Start".....
nothing will change...and what string of sequence has gone cant be used in Conditional Probability calculation of getting H...cause Collection is non-ending.


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 Fat Tails 
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vvhg View Post
Now you confused them completely.... Wait and see...

vvhg

I did not confuse @ devdas, and I answered his post. Some of the other readers may be confused, but I do not mind.

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 Fat Tails 
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devdas View Post
See, this is how, your game will compares with Infinite Cells of resistances...removing any number of cells doesn't changes the net resistance between points A and B.
What it simulates in given toss example....if one remove diagonally Ts...it will still have "Fresh Start".....
nothing will change...and what string of sequence has gone cant be used in Conditional Probability calculation of getting H...cause Collection is non-ending.


I was talking about conditional probabilities of finite subsets.

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 Lampert 
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traitor786 View Post
the question should be.

if a coin is fliped 3 times , and 2 heads show up, what are the chances that the next flip comes a head also.

since the last flip has not been made, do we just assume it is an individual flip at 50 50 or do we look at the previous flips and say that it is .5 to the power of 3 ?

In order for it to be a falasy it should go against common sence to some respect and common sence would state that the last flip is not a 50 50.

if you believe the last flip is a 50 50, then all flips are 50 50.

if that the case then why do we even quote the formulae .5 x .5 x .5 ?

maybe im just unclear on what side you are on or maybe im not understanding something here

OK, traitor, let me try this approach. All probabilities that are being discussed in this coin flip example are in the future. If the coin flip has already occurred then the probability of its result is 1.0 which is a certainty.

So if the flips have not been done, then the probability of H H H is 0.5 x 0.5 x 0.5 = 0.125

If the first two flips have been completed and they happen to come out as H H, the probability of another H is 0.5. The fact that two H occurred in the past has no effect on the outcome of the third flip. The gambler's fallacy suggests that a T is more likely on the third flip which is not true.


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 devdas 
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Fat Tails View Post
I was talking about conditional probabilities of finite subsets.

Your Welcome.

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traitor786
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Lampert View Post
OK, traitor, let me try this approach. All probabilities that are being discussed in this coin flip example are in the future. If the coin flip has already occurred then the probability of its result is 1.0 which is a certainty.

So if the flips have not been done, then the probability of H H H is 0.5 x 0.5 x 0.5 = 0.125

If the first two flips have been completed and they happen to come out as H H, the probability of another H is 0.5. The fact that two H occurred in the past has no effect on the outcome of the third flip. The gambler's fallacy suggests that a T is more likely on the third flip which is not true.


I understand what you are saying. Any flip has a 50 - 50 chance whether it is the first flip or the 10th. It is the laws of gravity airo dynamics and applied force. Nothing to do with math. Its random.

But then in a sequence things change. hhh is 0.125 suggesting that the flip after hhh has a 90% chance of being T. But since it is a flip and all flips have a 50 50 chance we have a conflict.

Does teh coin know if it is in a sequence ?

further all flips to some degree are in a sequence. It could be the first flip of the coins life and it will still be in a sequence as cone can chart all coin flips ever made on any coin and add this one to the data.

or it could be flips of the coins life time. To qualify as a set there is nothing saying that teh flips have to be within 10 secs apart.

if i take 3 coins and do 2 flips on each on and only one comes out HH then i take only that coin to my friends house and and bet him 80% of my money that it will be T will it be a high probability gamble ?

or am i still at 50 50

if i do 1000 coin tosses and end up with a 40-60 heads to tails situation what will happen when i change the coin. will the trend continue ?

can a coin be fliped with out having any previous data?

if the third flip has a .125 chance of being T then by definition the third flip. which can be said to stand on its own will not be 50 50 .

the definition of stand on its own and sequence here are off. and it may be impossible to judge if a flip is on its own aor part of a sequence we have not even seen.

we can calculate all flips world wide ever made as the sequence. we can count flips made this year only, we can calculate flips of quaters only we can even say its a set of any 50 50 bets not limited to coin tosses.

All of these are valid, the fact that we say this toss stands on its own or is part of a set has no bearing on the out come as our thoughts are not taken in account.. (or are they )


Single flip, or part of a set . not our choice.

To conclude, there are 2 possibilities, the toss is on its own or part of a sequence. the 2 contradict one another.
we cant just say it stands on its own because we feel like it. Also when a coin is tossed the results yield a 100% chance or being what ever it comes out to.

there is something missing here for randomness cant be predicted to 90 % and i dounght any one here would bet there 50% of there net worth on the third or 10th for that matter heads.

again i have not read all the posts maybe im missing something but trying to be open minded to both sides. i have no position on this at this point

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  #184 (permalink)
 Fat Tails 
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traitor786 View Post
I understand what you are saying. Any flip has a 50 - 50 chance whether it is the first flip or the 10th. It is the laws of gravity airo dynamics and applied force. Nothing to do with math. Its random.

If the person who throws the coin does not know any specific turns and twists to influence it, it should be random.


traitor786 View Post
But then in a sequence things change. hhh is 0.125 suggesting that the flip after hhh has a 90% chance of being T.

No, not really. I am afraid you are confusing things. There are different probabilities:

-> the probability that a regular coin hits tails: 50%
-> the probability that the coin in the third toss hits tails; 50%
-> the probability (prior to the start of the first coin toss) that a sequence of 3 toin cosses will produce T-T-T: 12.5%


traitor786 View Post
But since it is a flip and all flips have a 50 50 chance we have a conflict.
Does the coin know if it is in a sequence ?

I have asked one of my coins and it was not aware that it had been in a sequence. Probably Alzheimer. Also there is no conflict, because the coin has no memory.


traitor786 View Post
If i take 3 coins and do 2 flips on each on and only one comes out HH then i take only that coin to my friends house and and bet him 80% of my money that it will be T will it be a high probability gamble ? or am i still at 50 50

You are still at 50/50. The coin has no memory.


traitor786 View Post
if i do 1000 coin tosses and end up with a 40-60 heads to tails situation what will happen when i change the coin. will the trend continue ?

A 40-60 heads to tail situation would be an extremely rare event. Let us do some calculations for fun:

10 coin tosses: There are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 1024 possible outcomes. Out of these 1024 possible outcomes there are 10! /( 6! x 4!) = 210 outcomes which have 4 heads. Accordingly you will find 120 outcomes for 3 heads, 45 outcomes for 2 heads, 10 outcomes for 1 head and 1 outcome for zero heads. If I add this up, I will get a total of 386 outcomes out of 1024, which stand for 40% heads or less. The probability can be therefore given as

P( 40% or less heads out of 10 coin tosses) = 386 / 1024 = 37.7 %

The number of outcomes that I used above can be directly taken from the last row of Pascal's triangle, as shown below:



For 1000 trials it ain't no fun of calculating that same probability, but lucky enough I found a binomial distribution calculator, which is located here

Binomial Distribution: Probability Calculator

The cumulative probability that there are 400 heads or less is 1.3642320780 x E -10, or otherwise put it is below 0.000000013 %.

Did you imagine that you talked about an event, which will probably never happen in your lifetime? Screenshot of Binomial Distribution Calculator below.



I am not responding to the remainder of your posts, as unfortunately you were confusing a lot of things.

I would suggest to have a look at some basic notions of probability calculus and statistics.

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traitor786
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Fat Tails View Post
If the person who throws the coin does not know any specific turns and twists to influence it, it should be random.


No, not really. I am afraid you are confusing things. There are different probabilities:

-> the probability that a regular coin hits tails: 50%
-> the probability that the coin in the third toss hits tails; 50%
-> the probability (prior to the start of the first coin toss) that a sequence of 3 toin cosses will produce T-T-T: 12.5%


I have asked one of my coins and it was not aware that it had been in a sequence. Probably Alzheimer. Also there is no conflict, because the coin has no memory.


You are still at 50/50. The coin has no memory.

.

Sorry for my confusion. I have limited knowledge in this and am just looking at logic putting aside all else for now.

I understand this can be frustrating for some one who understands the math. But in order to keep an open mind, I like to figure out the logic before I decide what formulae to use or theory to follow.

There is a flaw in this. It may not be mathematical, maybe its wording. Or maybe the incorrect wording may lead us to the wrong theory/formulae. Theories are made to be proven incorrect.

You state

-> the probability that a regular coin hits tails: 50%
-> the probability that the coin in the third toss hits tails; 50%
-> the probability (prior to the start of the first coin toss) that a sequence of 3 toin cosses will produce T-T-T: 12.5%

Is it just me or is this a contradiction?

odds that a coin lands TTT is 12.5 % Or .5 x .5 x .5 = 12.5%

I understand that this is the formulae but we must question why are we multiplying?

you state that the probability that the 3rd coin lands T is 50% That means that you are not taking in to account the sequence.

But then you say that prior to the start of the first coin toss the odds are 12.5 %. So here we are looking at a sequence.

If the odds are 12.5% that this can occur that would give a greater possibility that it wont occur. As soon as you say odds of a sequence are less the 50 50 you are saying that there is an imbalance.

If you trade and 60% of your trades are successful, then you would assume that things will revert to 60%

Reverting implies that there is some memory of some sort. The coin can revert to 50 50 unless it knows how much it went off by in one direction.

If indeed it does revert, then once it is at an imbalance say 40 T-60 H odds are that there will be more T's popping up in order to revert back to the 50 50.

You say that the odds are 12.5% of a sequence coming out TTT BEFORE the flips. Why only before?

Will the coin change its mind during the sequence ? how does our intention to start calculating before or after effect the toss. Maybe the coin can read our mind ?

I'm just teasing cause of the remark you made about my coins with good memory.

On the other hand,

It should be noted that the odds of T-H-T is also 12.5 %

and so is T-T-H

so when there is T T
odds the next flip will be H or T is EQUAL or 50 50 as you state

but, the issue is odds that the coin will land on either heads or tails is 100%

how ever 12.5% plus 12.5% is 25% not 100%.

Maybe the issue is my (or our) understanding of odds. maybe the formulae of .5 to the power of 3 is incorrect.

But

The fact that the coin will revert back to 50 50 after many flips is spooky to me. This is not my definition of random. Randomness should not revert by definition.

Maybe coins do remember. Maybe that's why strip clubs do so well. cause the money is happy, and the money conditioned us to keep going.

I'm really not expecting any replies any more lol Maybe I'm just teaching my self calculus the hard way here. But I will do a test with a real coin.

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  #186 (permalink)
 Fat Tails 
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traitor786 View Post
You state

-> the probability that a regular coin hits tails: 50%
-> the probability that the coin in the third toss hits tails; 50%
-> the probability (prior to the start of the first coin toss) that a sequence of 3 toin cosses will produce T-T-T: 12.5%

Is it just me or is this a contradiction?

odds that a coin lands TTT is 12.5 % Or .5 x .5 x .5 = 12.5%

I understand that this is the formulae but we must question why are we multiplying?

We are multiplying, because the three toin cosses are independent of each other. Each toin coss has a probability of 50% of producing heads or tails. So any string - whether it is TTT or THT or HHH or HHT - has a probability of 12.5%.


traitor786 View Post
you state that the probability that the 3rd coin lands T is 50% That means that you are not taking in to account the sequence.

No I am looking at the single coin toss.


traitor786 View Post
But then you say that prior to the start of the first coin toss the odds are 12.5 %. So here we are looking at a sequence.

Correct, here I am looking at the sequence.


traitor786 View Post
If the odds are 12.5% that this can occur that would give a greater possibility that it wont occur. As soon as you say odds of a sequence are less the 50 50 you are saying that there is an imbalance.

Why? The odds of a sequence are not identical with the odds for a single toss. There is no imbalance.


traitor786 View Post
If you trade and 60% of your trades are successful, then you would assume that things will revert to 60%

Reverting implies that there is some memory of some sort. The coin can revert to 50 50 unless it knows how much it went off by in one direction.

If indeed it does revert, then once it is at an imbalance say 40 T-60 H odds are that there will be more T's popping up in order to revert back to the 50 50.

There is no reversion. Coins do not have a memory. If you toss a coin 1000 times and then 1000 times again, the second thousand tosses are independent from the result of the first 1000 tosses. Let us assume that the first 1000 tosses only produce 40% heads (very, very unlikely as shown in my prior post)

Then the next 1000 tosses are not affected by this, and will likely produce something around 50% of heads. The "reversion" is caused by the fact that after 2,000 tosses you now have 45% heads, 40% from the first series and 50% from the second series. But the second series was not affected by the first one.


traitor786 View Post
You say that the odds are 12.5% of a sequence coming out TTT BEFORE the flips. Why only before?

Before you do not know what will happen.

Probability for TTT before : 12.5%

Probability for TTT after the first coin toss with result heads: You now know that the 1st toss is heads. This reduces the probability for TTT to 0%.

Probability for TTT after the first coin toss with result tails: You now know that the 1st toss is tails. This increases the probability for TTT to 25%, as it now only depends on the second and third toss.


traitor786 View Post
It should be noted that the odds of T-H-T is also 12.5 %

and so is T-T-H

so when there is T T
odds the next flip will be H or T is EQUAL or 50 50 as you state

Correct.


traitor786 View Post
but, the issue is odds that the coin will land on either heads or tails is 100%

how ever 12.5% plus 12.5% is 25% not 100%.

Correct. The probability that the first two coin tosses produce TT is 25%.


traitor786 View Post
But the fact that the coin will revert back to 50 50 after many flips is spooky to me. This is not my definition of random. Randomness should not revert by definition.

As I said it is not reverting as this would be indeed spooky. The "reversion" does not affect the first series of tosses, it is just produced by the impact of averaging the first series with the second series.

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  #187 (permalink)
 Lornz 
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I don't mean to offend anyone, but I would recommend this book as a starting point for understanding the basic concepts of statistics and probability.

https://www.amazon.com/gp/product/0062731025/ref=as_li_ss_tl?ie=UTF8&tag=mark01f-20&linkCode=as2&camp=1789&creative=390957&creativeASIN=0062731025

Don't be fooled by the fact that it's a cartoon; I read it (too many) years ago, and it really is a good introduction. It's also quite funny.

The author, Larry Gonick (https://www.larrygonick.com/), has done books on a lot of other topics too: https://www.amazon.com/gp/entity/Larry-Gonick/B000AQ75IY/?ie=UTF8&tag=mark01f-20&linkCode=ur2&camp=1789&creative=390957

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  #188 (permalink)
AlgoGeek
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Hi guys,
First post...here you go.
My colleague, an Ivy League PhD. in mathematics, and I have built a model based upon these concepts (50/50 coin flip).
We appied our algorithms and intraday trading rules to a global liquid futures market stream of tick data (325,000 actual market prices). We never took a position home overnight and were indifferent about market direction from day to day or week to week.
What we found is that quite different from the casino wager in which player risks $1 for $1 gain (yes in some cases you can buy odds, double down, lay chips on double 4s, etc...different topic), in our "Game" we always win a larger quanitity than the market (casino) wins from us.
Having searched for micro patterns of behavioral tendencies we arrived at a very specific set of rules (algo sets if you will) which put the odds of making money in our favor. Not the odds of winning %, but of making money.
What we found was that the more risk we were willing to endure, in order to increase our win %, the larger the drawdowns (negative strings I guess you would say) were and the more randomness we were exposed to.
The most interesting set of results was that over an 18 month, 8000 trade analysis using over 325,000 price points from a market data source, with a 40.7% win percentage using an intial capital stake of $25,000.00, our "Game" made over $228,000.00 with a maximum negative string of just under $13,500.00 and not a single negative month. We did not model progressive betting/trading in order to capture these returns. Always the original bet.
Summary: Since we, the players, can tell the casino (market) how much they will pay us if we are right and how much we will pay them if we are wrong, we found an optimal algo set which won less than 50% of the time and yet 'beat' the casino (market) by over 16:1 margin. Seems to good to be true, I know, my cynical 68 yr old mentor already told me....until he saw the reports...anyway, too long winded already. We are thinking about how to proceed...meaning keep this automated system to ourselves or open it up to others to participate with us. No we can't share the code, sorry, way too much invested in that...but if you have any interest we may put together a list of contacts of folks who like us are interested in a solid automated trading system.
And yes I do have quite a few day trading and chart setup ideas which I am happy to share...just not the code.

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  #189 (permalink)
 Fat Tails 
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AlgoGeek View Post
Hi guys,
First post...here you go.
My colleague, an Ivy League PhD. in mathematics, and I have built a model based upon these concepts (50/50 coin flip).
We appied our algorithms and intraday trading rules to a global liquid futures market stream of tick data (325,000 actual market prices). We never took a position home overnight and were indifferent about market direction from day to day or week to week.
What we found is that quite different from the casino wager in which player risks $1 for $1 gain (yes in some cases you can buy odds, double down, lay chips on double 4s, etc...different topic), in our "Game" we always win a larger quanitity than the market (casino) wins from us.

Most of the casino games such as roulette are random games. As there is no strategy to win a random game with a negative expectation it is even useless to try. Black Jack is an exception, because due to the limited number of cards in a stack, the game is no more random when most of the cards have been played, but the expectation may shift into the positive territory.


AlgoGeek View Post
Having searched for micro patterns of behavioral tendencies we arrived at a very specific set of rules (algo sets if you will) which put the odds of making money in our favor. Not the odds of winning %, but of making money.
What we found was that the more risk we were willing to endure, in order to increase our win %, the larger the drawdowns (negative strings I guess you would say) were and the more randomness we were exposed to.
The most interesting set of results was that over an 18 month, 8000 trade analysis using over 325,000 price points from a market data source, with a 40.7% win percentage using an intial capital stake of $25,000.00, our "Game" made over $228,000.00 with a maximum negative string of just under $13,500.00 and not a single negative month. We did not model progressive betting/trading in order to capture these returns. Always the original bet.

Yes, I believe that there are micro pattern that you can observe and exploit. The question is only, if the population of traders and the species of algorithms will remain the same over the next 18 months. How will you adapt your rules, if they stop working because you have to share your meal with other carnivores?

Larger drawdowns are to be avoided because of their negative impact on progressive betting models. If you have a moderate edge, but relatively small drawdowns, you can easily leverage your returns by using an approach to bet half-Kelly.

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  #190 (permalink)
 Bermudan Option 
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So you cannot stack the odds in your favor by predicting strings. If that was the case, then it would be possible to 'stack' a future coin flip in your favor by purposefully creating a string beforehand that is biased towards your choice

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  #191 (permalink)
 cme4pif 
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It is odd to me that this thread became so focused on the subject of a string of outcomes and the odds of the next outcome argument, yet I think that the real important idea at the beginning of the thread was the idea that casinos don’t make there money based on the “edge” of the game but in fact do make there money based when the player runs out of money. Dr. Tharp and Ralph Vince talk about the risk of ruin even in a game 60% in your favour.
Here is a copy found all over the net:
https://www.otrader.com.au/dloads/difficultmakemoney.pdf

What this says is that a casino would still win even in a 50/50 game like coin toss.
Also in effect it says if you built an automated trading system that can win 60% of the time, if it bets a big part of your account, it will still blow up your account. We know this as getting through a drawdown.

All that is nothing new . . . but I have been thinking that a stop loss is a little bit like a mini blowing up of your account. You can build almost any automated trading system you like and if you introduce a stop loss in your back-test you will usually get a lower overall return.

In the bigger picture, if the market were full of traders with stops and many other traders with under-funded accounts, it would cause the market to drop faster than it rises, a phenonium we do see in the markets. Like a casino, a draw-down or string of bets loosing means the play must quit, this would cause funds to transfer to the “house” or in the market the better funded pros with better risk management. You can also say new money comes in to the market, but it just bounces around, until someone losses and steps away from the table. Fear and greed come in again. The amateurs would give up on the market just when they should buy. The old floor traders used to say, when you feel like you want to puke on your shoes, it’s probably time to buy more.

I recall years ago learning a fascinating idea, that a stock that has a lot of short interest can rocket up if the shorts get squeezed and they all must cover. Imagine the emotions of someone with a great short but the stock rises anyway (like Netflicks last year). They must feel just like the guy in Vegas when his ATM card says no more money for you. At some point you reach a pain threshold, margin call or just go broke. In a way, it is at this point your money is released back into the trading system. This happens not just to one trader but thousands at once. When the selling pressure is finally off, the stock must do something and when you are all out of sellers that something is the stock goes up in value.

I have thought about how you trade this, and it begins to sound like old trader wisdom, “buy on the pull back” and “keep your powder dry”. It even gets a bit like Warren Buffet. I have built a number of automated trading systems based on simple indicators, but the ones based on price using “pull backs” usually outperform. In a way you are buying at fire sale prices, buying low to sell high later. This really should not be a surprise that it works.

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  #192 (permalink)
 CRM5096 
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Peter2150 View Post
This thread reminds me of a remark made to me by a trading mentor. I had personal knowledge of his trading success, and he used several different indicators including a form of linear regression.

At the time he was trading a 5 minute SP chart, with no over night data. So using a 10 period linear regression indicator it was obvious if there was a big gap the indicator was very wrong the first 10 bars.

I wrote him and explained how the indicator was wrong and shouldn't be used in the first 10 bars if there was a gap. I'll never forget his answer.

It was, "If I understand all you do about this indicator, I might not use it to help me make money, but I don't understand what you are talking about, so I use it, and it does help me make money." This is a real trader talking.

So to me while the discussion about the advanced math and gaming theory is interesting, to me, wanting to improve my trading, it is really irrelevant.

Pete

"If I understand all you do about this indicator, I might not use it to help me make money, but I don't understand what you are talking about, so I use it, and it does help me make money."

i like that quote i added my own twist to it

"If I understand all you do about Patterns, Volume and Indicator's, I might not use them to help me make points, but I don't understand what you are talking about, so I use them, and it does help me make points."
CRM

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  #193 (permalink)
Steadfast Andy
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Fat Tails View Post
One last recommendation here for those who are interested: Well known Gambler and Hedge Fund Manager Edward O.Thorp has written a book on "The Mathematics of Gambling". You may download your personal (legal) copy here.

THE MATHEMATICS OF GAMBLING

Thanks for posting this. I really enjoyed skimming through it!

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  #194 (permalink)
 jonc 
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Steadfast Andy View Post
Fat Tails
One last recommendation here for those who are interested: Well known Gambler and Hedge Fund Manager Edward O.Thorp has written a book on "The Mathematics of Gambling". You may download your personal (legal) copy here.

THE MATHEMATICS OF GAMBLING

In the book which FT recommended, it is mentioned if you have the a 0.52 (p) probability of winning and the risk/reward is 1:1, the optimal bet size is calculated as p - (1- p).

If my risk/reward changes, how can I incorporate the r/r into the equation?

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  #195 (permalink)
 Hotch 
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Kelly criterion works for R:R.

(p*b-(1-p))/b

Where B is your R:R ratio. (so wins twice losses, b =2)

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  #196 (permalink)
 vvhg 
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Hotch View Post
Kelly criterion works for R:R.

(p*b-(1-p))/b

Where B is your R:R ratio. (so wins twice losses, b =2)

Lets say it factors in RR, whether the Kelly criterion works at all is debatable. Interesting results if you assume b=100 and b=2 at constant p for arguments sake....the practical risk of ruin is rather high using kelly but for high RR the practical risk of ruin gets unacceptably high.


Vvhg

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  #197 (permalink)
 Big Mike 
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Hotch View Post
Kelly criterion works for R:R.

(p*b-(1-p))/b

Where B is your R:R ratio. (so wins twice losses, b =2)

@Hotch (and other math guys) perhaps you can help us here:



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  #198 (permalink)
 Hotch 
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vvhg View Post
Lets say it factors in RR, whether the Kelly criterion works at all is debatable. Interesting results if you assume b=100 and b=2 at constant p for arguments sake....the practical risk of ruin is rather high using kelly but for high RR the practical risk of ruin gets unacceptably high.


Vvhg

It depends on your definition of "works", aka your personal goals, but mathematically it's still correct. The whole point of Kelly is that it is the maximum you should ever trade, because trading a larger size increases your risk without increasing your return (in the long run).

Of course, it's also assumes independent trades etc.

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  #199 (permalink)
 vvhg 
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Hotch View Post
It depends on your definition of "works", aka your personal goals, but mathematically it's still correct. The whole point of Kelly is that it is the maximum you should ever trade, because trading a larger size increases your risk without increasing your return (in the long run).

Of course, it's also assumes independent trades etc.

The main difficulty I have with kelly is the limitation to Bernoulli distributions, ie only two possible outcomes. This does not reflect the real world and results in too high bet sizes being suggested by Kelly.

Vvhg

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  #200 (permalink)
 jonc 
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Hi guys,

Is there a single factor/ratio which take into account of both Risk/Reward and probability?

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